Computational investigation of elliptic systems with discontinuous coefficients

2000 ◽  
Vol 36 (4) ◽  
pp. 605-609
Author(s):  
V. V. Skopetskii ◽  
S. I. Lyashko ◽  
S. A. Voitsekhovskiib
Keyword(s):  
Elliptic Systems ◽  
Discontinuous Coefficients ◽  
Computational Investigation

Continuity of the derivatives of solutions related to elliptic systems

2006 ◽  
Vol 136 (5) ◽  
pp. 1027-1039 ◽  
Author(s):  
Maria Alessandra Ragusa
Keyword(s):  
Lower Order ◽  
Morrey Space ◽  
Hölder Continuity ◽  
Elliptic Systems ◽  
Discontinuous Coefficients ◽  
Local Solution ◽  
Holder Continuity ◽  
Derivatives Of ◽  
Local Hölder Continuity

We consider elliptic systems with discontinuous coefficients and prove that if the known term belongs to the Morrey space Lp,λ, then the highest-order derivatives of the local solution belong to the same space. We also obtain local Hölder continuity for lower-order derivatives.

Regularity results for a priori bounded minimizers of non-autonomous functionals with discontinuous coefficients

2019 ◽  
Vol 12 (1) ◽  
pp. 85-110 ◽  
Author(s):  
Raffaella Giova ◽  
Antonia Passarelli di Napoli
Keyword(s):  
Sobolev Space ◽  
A Priori ◽  
Elliptic Systems ◽  
Discontinuous Coefficients ◽  
Growth Conditions ◽  
Integral Functionals ◽  
Local Minimizers ◽  
Higher Integrability ◽  
Regularity Results ◽  
Higher Differentiability

AbstractWe prove the higher differentiability and the higher integrability of the a priori bounded local minimizers of integral functionals of the form\mathcal{F}(v,\Omega)=\int_{\Omega}f(x,Dv(x))\,{\mathrm{d}}x,with convex integrand satisfyingp-growth conditions with respect to the gradient variable, assuming that the function that measures the oscillation of the integrand with respect to thex-variable belongs to a suitable Sobolev space. The a priori boundedness of the minimizers allows us to obtain the higher differentiability under a Sobolev assumption which is independent on the dimensionnand that, in the case{p\leq n-2}, improves previous known results. We also deal with solutions of elliptic systems with discontinuous coefficients under the so-called Uhlenbeck structure. In this case, it is well known that the solutions are locally bounded and therefore we obtain analogous regularity results without the a priori boundedness assumption.

Homogenization of the conormal derivative problem for elliptic systems in Reifenberg domains

2017 ◽  
Vol 20 (02) ◽  
pp. 1650062 ◽  
Author(s):  
Sun-Sig Byun ◽  
Yunsoo Jang
Keyword(s):  
Elliptic System ◽  
Bounded Domain ◽  
Elliptic Systems ◽  
Discontinuous Coefficients ◽  
Bounded Mean Oscillation ◽  
Derivative Problem ◽  
Mean Oscillation ◽  
Reifenberg Flat

We study homogenization of the conormal derivative problem for an elliptic system with discontinuous coefficients in a bounded domain. A uniform global [Formula: see text] estimate for [Formula: see text] is obtained under optimal assumptions that the coefficients have a small bounded mean oscillation (BMO) seminorm and the domain is a [Formula: see text]-Reifenberg flat domain whose boundary might be fractal.

Sign in / Sign up

Export Citation Format

Share Document